{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:A7MHMZIXFYC3MKMTELWI4GAVHU","short_pith_number":"pith:A7MHMZIX","canonical_record":{"source":{"id":"1612.03013","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-12-09T13:33:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c8dad34cacaac275da7abfd9382a544bb4aedef38287fc948caafc0ca6d44df1","abstract_canon_sha256":"e8dc79dec8b4b2be1604c0758a96afff2346705a93ed2359edfc88d0d46c8820"},"schema_version":"1.0"},"canonical_sha256":"07d87665172e05b6299322ec8e18153d1cd5acb803167c477a4dcb6c9fb1bb0d","source":{"kind":"arxiv","id":"1612.03013","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03013","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03013v3","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03013","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"pith_short_12","alias_value":"A7MHMZIXFYC3","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A7MHMZIXFYC3MKMT","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A7MHMZIX","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:A7MHMZIXFYC3MKMTELWI4GAVHU","target":"record","payload":{"canonical_record":{"source":{"id":"1612.03013","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-12-09T13:33:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c8dad34cacaac275da7abfd9382a544bb4aedef38287fc948caafc0ca6d44df1","abstract_canon_sha256":"e8dc79dec8b4b2be1604c0758a96afff2346705a93ed2359edfc88d0d46c8820"},"schema_version":"1.0"},"canonical_sha256":"07d87665172e05b6299322ec8e18153d1cd5acb803167c477a4dcb6c9fb1bb0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:21.085268Z","signature_b64":"VOiMt1tJs8Glv/mnoU01BtGgKhWyw3NVmNaygD11srs/lecTqFVvzWqmhAfUUMnrp9k+Nzz59XJb+29PAot1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07d87665172e05b6299322ec8e18153d1cd5acb803167c477a4dcb6c9fb1bb0d","last_reissued_at":"2026-05-18T00:29:21.084635Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:21.084635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.03013","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nh763nM61WvuGQr50ZsizS9Gt/LrnEmPlOW1fmfxppFGdD8PU3o8a9ht2m3fTQbPIvBxKJaL/l2/WjffSSPaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:22:12.724987Z"},"content_sha256":"5ada8f1b33cec3fb45a96b6a1aefc7897a0792402b4de38d4273768977ef2614","schema_version":"1.0","event_id":"sha256:5ada8f1b33cec3fb45a96b6a1aefc7897a0792402b4de38d4273768977ef2614"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:A7MHMZIXFYC3MKMTELWI4GAVHU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ornstein-Uhlenbeck Process with Fluctuating Damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Chai Hok Eab, S.C. Lim","submitted_at":"2016-12-09T13:33:29Z","abstract_excerpt":"This paper studies Langevin equation with random damping due to multiplicative noise and its solution. Two types of multiplicative noise, namely the dichotomous noise and fractional Gaussian noise are considered. Their solutions are obtained explicitly, with the expressions of the mean and covariance determined explicitly. Properties of the mean and covariance of the Ornstein-Uhlenbeck process with random damping, in particular the asymptotic behavior, are studied. The effect of the multiplicative noise on the stability property of the resulting processes is investigated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03013","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dDzYW9iXb06XjxbgX5v/ZCrL8X7QtRbskhrgLXHtQ1yezBmtyw7VnkSTYcNraGUyQ0GDr+Jg+Sue8OiLGyWVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:22:12.725534Z"},"content_sha256":"2175a25549d88a9fdf862bb2678698ed85097f706aff2bc578d8f9aed96bb82d","schema_version":"1.0","event_id":"sha256:2175a25549d88a9fdf862bb2678698ed85097f706aff2bc578d8f9aed96bb82d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A7MHMZIXFYC3MKMTELWI4GAVHU/bundle.json","state_url":"https://pith.science/pith/A7MHMZIXFYC3MKMTELWI4GAVHU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A7MHMZIXFYC3MKMTELWI4GAVHU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T20:22:12Z","links":{"resolver":"https://pith.science/pith/A7MHMZIXFYC3MKMTELWI4GAVHU","bundle":"https://pith.science/pith/A7MHMZIXFYC3MKMTELWI4GAVHU/bundle.json","state":"https://pith.science/pith/A7MHMZIXFYC3MKMTELWI4GAVHU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A7MHMZIXFYC3MKMTELWI4GAVHU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A7MHMZIXFYC3MKMTELWI4GAVHU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e8dc79dec8b4b2be1604c0758a96afff2346705a93ed2359edfc88d0d46c8820","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-12-09T13:33:29Z","title_canon_sha256":"c8dad34cacaac275da7abfd9382a544bb4aedef38287fc948caafc0ca6d44df1"},"schema_version":"1.0","source":{"id":"1612.03013","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03013","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03013v3","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03013","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"pith_short_12","alias_value":"A7MHMZIXFYC3","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A7MHMZIXFYC3MKMT","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A7MHMZIX","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:2175a25549d88a9fdf862bb2678698ed85097f706aff2bc578d8f9aed96bb82d","target":"graph","created_at":"2026-05-18T00:29:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper studies Langevin equation with random damping due to multiplicative noise and its solution. Two types of multiplicative noise, namely the dichotomous noise and fractional Gaussian noise are considered. Their solutions are obtained explicitly, with the expressions of the mean and covariance determined explicitly. Properties of the mean and covariance of the Ornstein-Uhlenbeck process with random damping, in particular the asymptotic behavior, are studied. The effect of the multiplicative noise on the stability property of the resulting processes is investigated.","authors_text":"Chai Hok Eab, S.C. Lim","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-12-09T13:33:29Z","title":"Ornstein-Uhlenbeck Process with Fluctuating Damping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03013","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5ada8f1b33cec3fb45a96b6a1aefc7897a0792402b4de38d4273768977ef2614","target":"record","created_at":"2026-05-18T00:29:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e8dc79dec8b4b2be1604c0758a96afff2346705a93ed2359edfc88d0d46c8820","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-12-09T13:33:29Z","title_canon_sha256":"c8dad34cacaac275da7abfd9382a544bb4aedef38287fc948caafc0ca6d44df1"},"schema_version":"1.0","source":{"id":"1612.03013","kind":"arxiv","version":3}},"canonical_sha256":"07d87665172e05b6299322ec8e18153d1cd5acb803167c477a4dcb6c9fb1bb0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07d87665172e05b6299322ec8e18153d1cd5acb803167c477a4dcb6c9fb1bb0d","first_computed_at":"2026-05-18T00:29:21.084635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:21.084635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VOiMt1tJs8Glv/mnoU01BtGgKhWyw3NVmNaygD11srs/lecTqFVvzWqmhAfUUMnrp9k+Nzz59XJb+29PAot1Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:21.085268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.03013","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ada8f1b33cec3fb45a96b6a1aefc7897a0792402b4de38d4273768977ef2614","sha256:2175a25549d88a9fdf862bb2678698ed85097f706aff2bc578d8f9aed96bb82d"],"state_sha256":"959eecd3009a0ebaa85dc20e8def820890efef5aa418f89cc649ea033336680a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vxByagb0/G3xLEYCtm0w9+k9volqJ7qTpL/yJxwy4nKuH0+41JwSuSB8tVX9ZCCWxAUsL60WNVuAlFmicFbUCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T20:22:12.728116Z","bundle_sha256":"bf6edd2d324151b8f8b3b7212596dfa17b8b9804dce0d34552db2e3f87e7df6d"}}